论文标题
柔和图表的定期分区
Regular partitions of gentle graphs
论文作者
论文摘要
Szemeredi的规律性引理是极端组合学的非常有用的工具。最近，对于特殊的，更结构化的图形类别，获得了该精液结果的几种改进。我们在其丰富的组合环境中调查这些结果。特别是，我们强调与（结构）稀疏理论的联系，这导致了开放问题的替代证明，改进和解决方案。有趣的是，其中许多班级都带来了具有挑战性的问题。然而，从规律性引理类型陈述的角度来看，它们似乎是“温柔”的课程。
Szemeredi's Regularity Lemma is a very useful tool of extremal combinatorics. Recently, several refinements of this seminal result were obtained for special, more structured classes of graphs. We survey these results in their rich combinatorial context. In particular, we stress the link to the theory of (structural) sparsity, which leads to alternative proofs, refinements and solutions of open problems. It is interesting to note that many of these classes present challenging problems. Nevertheless, from the point of view of regularity lemma type statements, they appear as "gentle" classes.
